Worksheet: Distribution of Molecular Speeds

In this worksheet, we will practice calculating the proportion of particles, in an ideal gas, that have a given speed using the Maxwell–Boltzmann distribution function.

Q1:

An incandescent light bulb is filled with neon gas. The gas that is in close proximity
to the element of the bulb is at a temperature of
2,300 K. Determine the root-mean-square
speed of neon atoms in close proximity to the element.
Use a value of 20.2 g/mol for the molar mass of neon.

A1.7×10 m/s

B4.5×10 m/s

C3.6×10 m/s

D3.2×10 m/s

E22×10 m/s

Q2:

Helium atoms in a gas that is at a temperature 𝑇 have a root-mean-square speed
of 196 m/s. When the gas is heated until it becomes a plasma with a temperature 𝑇,
the root-mean-square speed of the helium atoms is 618 km/s.
Use a value of 4.003 g/mol for the molar mass of helium.

Find 𝑇.

Find 𝑇.

A6.13×10 K

B3.68×10 K

C63.7×10 K

D6.17×10 K

E6.59×10 K

Q3:

Using the approximation
𝑓(𝑣)𝑣≈𝑓(𝑣)Δ𝑣d for small
Δ𝑣, estimate the
fraction of nitrogen molecules at a temperature of
3.00×10 K
that have
speeds between 290 m/s
and 291 m/s.
A nitrogen molecule has a mass of 4.65×10 kg.

Q4:

Find the ratio 𝑓𝑣𝑓(𝑣)prms for hydrogen gas at a
temperature of 77.0 K. Use a molar mass
of 2.02 g/mol for hydrogen gas.

Q5:

In a sample of a monatomic gas, a number of molecules 𝑛 have
speeds that are within a very small range around the root-mean-square speed
of atoms in the gas, 𝑣.
A number of molecules 𝑛 have speeds that are
within the same very small range around a speed of 3.00⋅𝑣.
Determine the ratio of 𝑛 to 𝑛.

Q6:

A sample of nitrogen is at a temperature of
3,015 K.
N2 has a molar mass of 28.00 g/mol.